Multiple steady states, complex oscillations, and the devil’s staircase in the peroxidase–oxidase reaction

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Abstract
The steady and oscillatory states of the Olsen and Degn model for the peroxidase–oxidase oscillator are found. The stability of the steady states is determined, and a bifurcation diagram for the oscillatory regime is found. A complex sequence of multiply periodic oscillations is observed and found to follow an orderly pattern when described via the firing number, the number of small oscillations divided by the total number of large and small oscillations per period. A plot of the firing number vs one of the system parameters is found to have a stairstep relationship and it is shown that this stairstep relationship is a complete devil’s staircase, an infinite self‐similar staircase with chaotic properties and a fractal dimension.